Title:Nonthermal states arising from confinement in one and two dimensions

Abstract: We show that confinement in the quantum Ising model leads to nonthermal
eigenstates, in both continuum and lattice theories, in both one (1D) and two
dimensions (2D). In the ordered phase, the presence of a confining longitudinal
field leads to a profound restructuring of the excitation spectrum, with the
low-energy two-particle continuum being replaced by discrete 'meson' modes
(linearly confined pairs of domain walls). These modes exist far into the
spectrum and are atypical, in the sense that expectation values in the state
with energy $E$ do not agree with the microcanonical (thermal) ensemble
prediction. Single meson states persist above the two meson threshold, due to a
surprising lack of hybridization with the ($n\geq4$)-domain wall continuum, a
result that survives into the thermodynamic limit and that can be understood
from analytical calculations. The presence of such states is revealed in
anomalous post-quench dynamics, such as the lack of a light cone, the
suppression of the growth of entanglement entropy, and the absence of
thermalization for some initial states. The nonthermal states are confined to
the ordered phase - the disordered (paramagnetic) phase exhibits typical
thermalization patterns in both 1D and 2D in the absence of integrability.